Wormholes can effectively connect the fracture system as the dominant channels when carbonate matrix is acidified, thereby increasing the distance of acidification. It is critical to clarify the wormhole propagation law in carbonate reservoirs so as to optimize the acidification design. Previous studies highlight the influences of matrix as well as single simple fracture on wormhole propagation. However, the works characterizing impacts of single and multiple fractures with different geometry are insufficient. In this paper, the two-scale continuum model and pseudo-fracture model were combined to study the worm-hole with different fractures. It was found that the fractures parallel to injection direction can concentrate fluids and thus accelerate the acid penetrating the formation, while the perpendicular ones will disperse fluids, thereby slowing down the breakthrough. The effect of straight fractures and arc fractures on wormholes are similar. When the inclination angle is less than 60 degrees, straight fracture and arc fracture can be regarded as parallel fracture of corresponding length. When the inclination angle is greater than 60 degrees, they can be regarded as superposition of parallel fracture and perpendicular fracture. As for the circular and polygonal fractures, only the parts near the outlet impact the subsequent wormhole propagation trajectories. The analysis of flow field shows that there is a control domain of about 3.L.cos(theta) around the fractures. When there is no intersection of control domains of multiple fractures, there is no interference between them. There is no need to consider all fractures in the formation. Based on this, the step-by-step calculation method proposed in this paper is suitable for acidizing large-scale formation with complex fracture network. (C) 2019 Elsevier Ltd. All rights reserved.